Time shifting a signal

When a signal can be expressed in the form

$$y(n) = x(n-M),$$

$y(n)$ is a delayed (time-shifted) version of $x(n)$.

$y(n) = x(n-M)$: $x(n)$ is delayed $M$ samples:

• shift is to the right on the time axis.

$y(n) = x(n+M)$: $x(n)$ is advanced $M$ samples:

• shift is to the left on the time axis.